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Electronic Journal of Combinatorics
Article . 2011 . Peer-reviewed
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Article . 2011
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https://dx.doi.org/10.48550/ar...
Article . 2010
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Characterizations of Transversal and Fundamental Transversal Matroids

Characterizations of transversal and fundamental transversal matroids
Authors: Joseph E. Bonin; Joseph P. S. Kung; Anna de Mier;

Characterizations of Transversal and Fundamental Transversal Matroids

Abstract

A result of Mason, as refined by Ingleton, characterizes transversal matroids as the matroids that satisfy a set of inequalities that relate the ranks of intersections and unions of nonempty sets of cyclic flats. We prove counterparts, for fundamental transversal matroids, of this and other characterizations of transversal matroids. In particular, we show that fundamental transversal matroids are precisely the matroids that yield equality in Mason's inequalities and we deduce a characterization of fundamental transversal matroids due to Brylawski from this simpler characterization.

Keywords

FOS: Mathematics, Mason's inequalities, Mathematics - Combinatorics, Combinatorics (math.CO), Combinatorial aspects of matroids and geometric lattices, Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.), 05B35

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
Green
gold